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JEE Main201911 Jan 2019Evening ShiftMathematicsBinomial TheoremActual

Let (x+10)⁵⁰+(x-10)⁵⁰= a ₀+ a ₁ x+ a ₂ x²+ .+ a ₅₀ x⁵⁰ , for all x R ; then a ₂ a ₀ is equal to :

Options

  1. A12.5
  2. B12
  3. C12.25
  4. D12.75

Correct answer

C. 12.25

Step-by-step solution

(x+10)⁵⁰+(x-10)⁵⁰=a₀+a₁ x+a₂ x²+ +a₅₀ x⁵⁰ a₀+a₁ x+a₂ x²+ +a₅₀ x⁵⁰=2 ( 50 0 x⁵⁰+ 50 2 x⁴⁸ 10²+ 50 4 x⁴⁶ 10⁴+ ) a₀=2 50 50 10⁵⁰ a₂=2 50 2 10⁴⁸ a₂ a₀ = 50 2 10⁴⁸ 50 50 10⁵⁰ = 50 49 2 100 = 49 4 =12.25

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